<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2011 PHPExcel
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * @category    PHPExcel
 * @package        PHPExcel_Calculation
 * @copyright    Copyright (c) 2006 - 2011 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license        http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
 * @version        1.7.6, 2011-02-27
 */


/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {
    /**
     * @ignore
     */
    define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
    require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
}


/** EULER */
define('EULER', 2.71828182845904523536);


/**
 * PHPExcel_Calculation_Engineering
 *
 * @category    PHPExcel
 * @package        PHPExcel_Calculation
 * @copyright    Copyright (c) 2006 - 2011 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation_Engineering {

    private static $_conversionUnits = array( 'g'        => array(    'Group'    => 'Mass',            'Unit Name'    => 'Gram',                        'AllowPrefix'    => True        ),
                                              'sg'        => array(    'Group'    => 'Mass',            'Unit Name'    => 'Slug',                        'AllowPrefix'    => False    ),
                                              'lbm'        => array(    'Group'    => 'Mass',            'Unit Name'    => 'Pound mass (avoirdupois)',    'AllowPrefix'    => False    ),
                                              'u'        => array(    'Group'    => 'Mass',            'Unit Name'    => 'U (atomic mass unit)',        'AllowPrefix'    => True        ),
                                              'ozm'        => array(    'Group'    => 'Mass',            'Unit Name'    => 'Ounce mass (avoirdupois)',    'AllowPrefix'    => False    ),
                                              'm'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Meter',                        'AllowPrefix'    => True        ),
                                              'mi'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Statute mile',                'AllowPrefix'    => False    ),
                                              'Nmi'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Nautical mile',                'AllowPrefix'    => False    ),
                                              'in'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Inch',                        'AllowPrefix'    => False    ),
                                              'ft'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Foot',                        'AllowPrefix'    => False    ),
                                              'yd'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Yard',                        'AllowPrefix'    => False    ),
                                              'ang'        => array(    'Group'    => 'Distance',        'Unit Name'    => 'Angstrom',                    'AllowPrefix'    => True        ),
                                              'Pica'    => array(    'Group'    => 'Distance',        'Unit Name'    => 'Pica (1/72 in)',            'AllowPrefix'    => False    ),
                                              'yr'        => array(    'Group'    => 'Time',            'Unit Name'    => 'Year',                        'AllowPrefix'    => False    ),
                                              'day'        => array(    'Group'    => 'Time',            'Unit Name'    => 'Day',                        'AllowPrefix'    => False    ),
                                              'hr'        => array(    'Group'    => 'Time',            'Unit Name'    => 'Hour',                        'AllowPrefix'    => False    ),
                                              'mn'        => array(    'Group'    => 'Time',            'Unit Name'    => 'Minute',                    'AllowPrefix'    => False    ),
                                              'sec'        => array(    'Group'    => 'Time',            'Unit Name'    => 'Second',                    'AllowPrefix'    => True        ),
                                              'Pa'        => array(    'Group'    => 'Pressure',        'Unit Name'    => 'Pascal',                    'AllowPrefix'    => True        ),
                                              'p'        => array(    'Group'    => 'Pressure',        'Unit Name'    => 'Pascal',                    'AllowPrefix'    => True        ),
                                              'atm'        => array(    'Group'    => 'Pressure',        'Unit Name'    => 'Atmosphere',                'AllowPrefix'    => True        ),
                                              'at'        => array(    'Group'    => 'Pressure',        'Unit Name'    => 'Atmosphere',                'AllowPrefix'    => True        ),
                                              'mmHg'    => array(    'Group'    => 'Pressure',        'Unit Name'    => 'mm of Mercury',                'AllowPrefix'    => True        ),
                                              'N'        => array(    'Group'    => 'Force',            'Unit Name'    => 'Newton',                    'AllowPrefix'    => True        ),
                                              'dyn'        => array(    'Group'    => 'Force',            'Unit Name'    => 'Dyne',                        'AllowPrefix'    => True        ),
                                              'dy'        => array(    'Group'    => 'Force',            'Unit Name'    => 'Dyne',                        'AllowPrefix'    => True        ),
                                              'lbf'        => array(    'Group'    => 'Force',            'Unit Name'    => 'Pound force',                'AllowPrefix'    => False    ),
                                              'J'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Joule',                        'AllowPrefix'    => True        ),
                                              'e'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Erg',                        'AllowPrefix'    => True        ),
                                              'c'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Thermodynamic calorie',        'AllowPrefix'    => True        ),
                                              'cal'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'IT calorie',                'AllowPrefix'    => True        ),
                                              'eV'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Electron volt',                'AllowPrefix'    => True        ),
                                              'ev'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Electron volt',                'AllowPrefix'    => True        ),
                                              'HPh'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Horsepower-hour',            'AllowPrefix'    => False    ),
                                              'hh'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Horsepower-hour',            'AllowPrefix'    => False    ),
                                              'Wh'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Watt-hour',                    'AllowPrefix'    => True        ),
                                              'wh'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Watt-hour',                    'AllowPrefix'    => True        ),
                                              'flb'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'Foot-pound',                'AllowPrefix'    => False    ),
                                              'BTU'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'BTU',                        'AllowPrefix'    => False    ),
                                              'btu'        => array(    'Group'    => 'Energy',        'Unit Name'    => 'BTU',                        'AllowPrefix'    => False    ),
                                              'HP'        => array(    'Group'    => 'Power',            'Unit Name'    => 'Horsepower',                'AllowPrefix'    => False    ),
                                              'h'        => array(    'Group'    => 'Power',            'Unit Name'    => 'Horsepower',                'AllowPrefix'    => False    ),
                                              'W'        => array(    'Group'    => 'Power',            'Unit Name'    => 'Watt',                        'AllowPrefix'    => True        ),
                                              'w'        => array(    'Group'    => 'Power',            'Unit Name'    => 'Watt',                        'AllowPrefix'    => True        ),
                                              'T'        => array(    'Group'    => 'Magnetism',        'Unit Name'    => 'Tesla',                        'AllowPrefix'    => True        ),
                                              'ga'        => array(    'Group'    => 'Magnetism',        'Unit Name'    => 'Gauss',                        'AllowPrefix'    => True        ),
                                              'C'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Celsius',                    'AllowPrefix'    => False    ),
                                              'cel'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Celsius',                    'AllowPrefix'    => False    ),
                                              'F'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Fahrenheit',                'AllowPrefix'    => False    ),
                                              'fah'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Fahrenheit',                'AllowPrefix'    => False    ),
                                              'K'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Kelvin',                    'AllowPrefix'    => False    ),
                                              'kel'        => array(    'Group'    => 'Temperature',    'Unit Name'    => 'Kelvin',                    'AllowPrefix'    => False    ),
                                              'tsp'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Teaspoon',                    'AllowPrefix'    => False    ),
                                              'tbs'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Tablespoon',                'AllowPrefix'    => False    ),
                                              'oz'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Fluid Ounce',                'AllowPrefix'    => False    ),
                                              'cup'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Cup',                        'AllowPrefix'    => False    ),
                                              'pt'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'U.S. Pint',                    'AllowPrefix'    => False    ),
                                              'us_pt'    => array(    'Group'    => 'Liquid',        'Unit Name'    => 'U.S. Pint',                    'AllowPrefix'    => False    ),
                                              'uk_pt'    => array(    'Group'    => 'Liquid',        'Unit Name'    => 'U.K. Pint',                    'AllowPrefix'    => False    ),
                                              'qt'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Quart',                        'AllowPrefix'    => False    ),
                                              'gal'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Gallon',                    'AllowPrefix'    => False    ),
                                              'l'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Litre',                        'AllowPrefix'    => True        ),
                                              'lt'        => array(    'Group'    => 'Liquid',        'Unit Name'    => 'Litre',                        'AllowPrefix'    => True        )
                                            );

    private static $_conversionMultipliers = array(    'Y'    => array(    'multiplier'    => 1E24,    'name'    => 'yotta'    ),
                                                    'Z'    => array(    'multiplier'    => 1E21,    'name'    => 'zetta'    ),
                                                    'E'    => array(    'multiplier'    => 1E18,    'name'    => 'exa'    ),
                                                    'P'    => array(    'multiplier'    => 1E15,    'name'    => 'peta'    ),
                                                    'T'    => array(    'multiplier'    => 1E12,    'name'    => 'tera'    ),
                                                    'G'    => array(    'multiplier'    => 1E9,        'name'    => 'giga'    ),
                                                    'M'    => array(    'multiplier'    => 1E6,        'name'    => 'mega'    ),
                                                    'k'    => array(    'multiplier'    => 1E3,        'name'    => 'kilo'    ),
                                                    'h'    => array(    'multiplier'    => 1E2,        'name'    => 'hecto'    ),
                                                    'e'    => array(    'multiplier'    => 1E1,        'name'    => 'deka'    ),
                                                    'd'    => array(    'multiplier'    => 1E-1,    'name'    => 'deci'    ),
                                                    'c'    => array(    'multiplier'    => 1E-2,    'name'    => 'centi'    ),
                                                    'm'    => array(    'multiplier'    => 1E-3,    'name'    => 'milli'    ),
                                                    'u'    => array(    'multiplier'    => 1E-6,    'name'    => 'micro'    ),
                                                    'n'    => array(    'multiplier'    => 1E-9,    'name'    => 'nano'    ),
                                                    'p'    => array(    'multiplier'    => 1E-12,    'name'    => 'pico'    ),
                                                    'f'    => array(    'multiplier'    => 1E-15,    'name'    => 'femto'    ),
                                                    'a'    => array(    'multiplier'    => 1E-18,    'name'    => 'atto'    ),
                                                    'z'    => array(    'multiplier'    => 1E-21,    'name'    => 'zepto'    ),
                                                    'y'    => array(    'multiplier'    => 1E-24,    'name'    => 'yocto'    )
                                                 );

    private static $_unitConversions = array(    'Mass'        => array(    'g'        => array(    'g'        => 1.0,
                                                                                            'sg'    => 6.85220500053478E-05,
                                                                                            'lbm'    => 2.20462291469134E-03,
                                                                                            'u'        => 6.02217000000000E+23,
                                                                                            'ozm'    => 3.52739718003627E-02
                                                                                        ),
                                                                        'sg'    => array(    'g'        => 1.45938424189287E+04,
                                                                                            'sg'    => 1.0,
                                                                                            'lbm'    => 3.21739194101647E+01,
                                                                                            'u'        => 8.78866000000000E+27,
                                                                                            'ozm'    => 5.14782785944229E+02
                                                                                        ),
                                                                        'lbm'    => array(    'g'        => 4.5359230974881148E+02,
                                                                                            'sg'    => 3.10810749306493E-02,
                                                                                            'lbm'    => 1.0,
                                                                                            'u'        => 2.73161000000000E+26,
                                                                                            'ozm'    => 1.60000023429410E+01
                                                                                        ),
                                                                        'u'        => array(    'g'        => 1.66053100460465E-24,
                                                                                            'sg'    => 1.13782988532950E-28,
                                                                                            'lbm'    => 3.66084470330684E-27,
                                                                                            'u'        => 1.0,
                                                                                            'ozm'    => 5.85735238300524E-26
                                                                                        ),
                                                                        'ozm'    => array(    'g'        => 2.83495152079732E+01,
                                                                                            'sg'    => 1.94256689870811E-03,
                                                                                            'lbm'    => 6.24999908478882E-02,
                                                                                            'u'        => 1.70725600000000E+25,
                                                                                            'ozm'    => 1.0
                                                                                        )
                                                                    ),
                                                'Distance'    => array(    'm'        => array(    'm'        => 1.0,
                                                                                            'mi'    => 6.21371192237334E-04,
                                                                                            'Nmi'    => 5.39956803455724E-04,
                                                                                            'in'    => 3.93700787401575E+01,
                                                                                            'ft'    => 3.28083989501312E+00,
                                                                                            'yd'    => 1.09361329797891E+00,
                                                                                            'ang'    => 1.00000000000000E+10,
                                                                                            'Pica'    => 2.83464566929116E+03
                                                                                        ),
                                                                        'mi'    => array(    'm'        => 1.60934400000000E+03,
                                                                                            'mi'    => 1.0,
                                                                                            'Nmi'    => 8.68976241900648E-01,
                                                                                            'in'    => 6.33600000000000E+04,
                                                                                            'ft'    => 5.28000000000000E+03,
                                                                                            'yd'    => 1.76000000000000E+03,
                                                                                            'ang'    => 1.60934400000000E+13,
                                                                                            'Pica'    => 4.56191999999971E+06
                                                                                        ),
                                                                        'Nmi'    => array(    'm'        => 1.85200000000000E+03,
                                                                                            'mi'    => 1.15077944802354E+00,
                                                                                            'Nmi'    => 1.0,
                                                                                            'in'    => 7.29133858267717E+04,
                                                                                            'ft'    => 6.07611548556430E+03,
                                                                                            'yd'    => 2.02537182785694E+03,
                                                                                            'ang'    => 1.85200000000000E+13,
                                                                                            'Pica'    => 5.24976377952723E+06
                                                                                        ),
                                                                        'in'    => array(    'm'        => 2.54000000000000E-02,
                                                                                            'mi'    => 1.57828282828283E-05,
                                                                                            'Nmi'    => 1.37149028077754E-05,
                                                                                            'in'    => 1.0,
                                                                                            'ft'    => 8.33333333333333E-02,
                                                                                            'yd'    => 2.77777777686643E-02,
                                                                                            'ang'    => 2.54000000000000E+08,
                                                                                            'Pica'    => 7.19999999999955E+01
                                                                                        ),
                                                                        'ft'    => array(    'm'        => 3.04800000000000E-01,
                                                                                            'mi'    => 1.89393939393939E-04,
                                                                                            'Nmi'    => 1.64578833693305E-04,
                                                                                            'in'    => 1.20000000000000E+01,
                                                                                            'ft'    => 1.0,
                                                                                            'yd'    => 3.33333333223972E-01,
                                                                                            'ang'    => 3.04800000000000E+09,
                                                                                            'Pica'    => 8.63999999999946E+02
                                                                                        ),
                                                                        'yd'    => array(    'm'        => 9.14400000300000E-01,
                                                                                            'mi'    => 5.68181818368230E-04,
                                                                                            'Nmi'    => 4.93736501241901E-04,
                                                                                            'in'    => 3.60000000118110E+01,
                                                                                            'ft'    => 3.00000000000000E+00,
                                                                                            'yd'    => 1.0,
                                                                                            'ang'    => 9.14400000300000E+09,
                                                                                            'Pica'    => 2.59200000085023E+03
                                                                                        ),
                                                                        'ang'    => array(    'm'        => 1.00000000000000E-10,
                                                                                            'mi'    => 6.21371192237334E-14,
                                                                                            'Nmi'    => 5.39956803455724E-14,
                                                                                            'in'    => 3.93700787401575E-09,
                                                                                            'ft'    => 3.28083989501312E-10,
                                                                                            'yd'    => 1.09361329797891E-10,
                                                                                            'ang'    => 1.0,
                                                                                            'Pica'    => 2.83464566929116E-07
                                                                                        ),
                                                                        'Pica'    => array(    'm'        => 3.52777777777800E-04,
                                                                                            'mi'    => 2.19205948372629E-07,
                                                                                            'Nmi'    => 1.90484761219114E-07,
                                                                                            'in'    => 1.38888888888898E-02,
                                                                                            'ft'    => 1.15740740740748E-03,
                                                                                            'yd'    => 3.85802469009251E-04,
                                                                                            'ang'    => 3.52777777777800E+06,
                                                                                            'Pica'    => 1.0
                                                                                        )
                                                                    ),
                                                'Time'        => array(    'yr'    => array(    'yr'        => 1.0,
                                                                                            'day'        => 365.25,
                                                                                            'hr'        => 8766.0,
                                                                                            'mn'        => 525960.0,
                                                                                            'sec'        => 31557600.0
                                                                                        ),
                                                                        'day'    => array(    'yr'        => 2.73785078713210E-03,
                                                                                            'day'        => 1.0,
                                                                                            'hr'        => 24.0,
                                                                                            'mn'        => 1440.0,
                                                                                            'sec'        => 86400.0
                                                                                        ),
                                                                        'hr'    => array(    'yr'        => 1.14077116130504E-04,
                                                                                            'day'        => 4.16666666666667E-02,
                                                                                            'hr'        => 1.0,
                                                                                            'mn'        => 60.0,
                                                                                            'sec'        => 3600.0
                                                                                        ),
                                                                        'mn'    => array(    'yr'        => 1.90128526884174E-06,
                                                                                            'day'        => 6.94444444444444E-04,
                                                                                            'hr'        => 1.66666666666667E-02,
                                                                                            'mn'        => 1.0,
                                                                                            'sec'        => 60.0
                                                                                        ),
                                                                        'sec'    => array(    'yr'        => 3.16880878140289E-08,
                                                                                            'day'        => 1.15740740740741E-05,
                                                                                            'hr'        => 2.77777777777778E-04,
                                                                                            'mn'        => 1.66666666666667E-02,
                                                                                            'sec'        => 1.0
                                                                                        )
                                                                    ),
                                                'Pressure'    => array(    'Pa'    => array(    'Pa'        => 1.0,
                                                                                            'p'            => 1.0,
                                                                                            'atm'        => 9.86923299998193E-06,
                                                                                            'at'        => 9.86923299998193E-06,
                                                                                            'mmHg'        => 7.50061707998627E-03
                                                                                        ),
                                                                        'p'        => array(    'Pa'        => 1.0,
                                                                                            'p'            => 1.0,
                                                                                            'atm'        => 9.86923299998193E-06,
                                                                                            'at'        => 9.86923299998193E-06,
                                                                                            'mmHg'        => 7.50061707998627E-03
                                                                                        ),
                                                                        'atm'    => array(    'Pa'        => 1.01324996583000E+05,
                                                                                            'p'            => 1.01324996583000E+05,
                                                                                            'atm'        => 1.0,
                                                                                            'at'        => 1.0,
                                                                                            'mmHg'        => 760.0
                                                                                        ),
                                                                        'at'    => array(    'Pa'        => 1.01324996583000E+05,
                                                                                            'p'            => 1.01324996583000E+05,
                                                                                            'atm'        => 1.0,
                                                                                            'at'        => 1.0,
                                                                                            'mmHg'        => 760.0
                                                                                        ),
                                                                        'mmHg'    => array(    'Pa'        => 1.33322363925000E+02,
                                                                                            'p'            => 1.33322363925000E+02,
                                                                                            'atm'        => 1.31578947368421E-03,
                                                                                            'at'        => 1.31578947368421E-03,
                                                                                            'mmHg'        => 1.0
                                                                                        )
                                                                    ),
                                                'Force'        => array(    'N'        => array(    'N'            => 1.0,
                                                                                            'dyn'        => 1.0E+5,
                                                                                            'dy'        => 1.0E+5,
                                                                                            'lbf'        => 2.24808923655339E-01
                                                                                        ),
                                                                        'dyn'    => array(    'N'            => 1.0E-5,
                                                                                            'dyn'        => 1.0,
                                                                                            'dy'        => 1.0,
                                                                                            'lbf'        => 2.24808923655339E-06
                                                                                        ),
                                                                        'dy'    => array(    'N'            => 1.0E-5,
                                                                                            'dyn'        => 1.0,
                                                                                            'dy'        => 1.0,
                                                                                            'lbf'        => 2.24808923655339E-06
                                                                                        ),
                                                                        'lbf'    => array(    'N'            => 4.448222,
                                                                                            'dyn'        => 4.448222E+5,
                                                                                            'dy'        => 4.448222E+5,
                                                                                            'lbf'        => 1.0
                                                                                        )
                                                                    ),
                                                'Energy'    => array(    'J'        => array(    'J'            => 1.0,
                                                                                            'e'            => 9.99999519343231E+06,
                                                                                            'c'            => 2.39006249473467E-01,
                                                                                            'cal'        => 2.38846190642017E-01,
                                                                                            'eV'        => 6.24145700000000E+18,
                                                                                            'ev'        => 6.24145700000000E+18,
                                                                                            'HPh'        => 3.72506430801000E-07,
                                                                                            'hh'        => 3.72506430801000E-07,
                                                                                            'Wh'        => 2.77777916238711E-04,
                                                                                            'wh'        => 2.77777916238711E-04,
                                                                                            'flb'        => 2.37304222192651E+01,
                                                                                            'BTU'        => 9.47815067349015E-04,
                                                                                            'btu'        => 9.47815067349015E-04
                                                                                        ),
                                                                        'e'        => array(    'J'            => 1.00000048065700E-07,
                                                                                            'e'            => 1.0,
                                                                                            'c'            => 2.39006364353494E-08,
                                                                                            'cal'        => 2.38846305445111E-08,
                                                                                            'eV'        => 6.24146000000000E+11,
                                                                                            'ev'        => 6.24146000000000E+11,
                                                                                            'HPh'        => 3.72506609848824E-14,
                                                                                            'hh'        => 3.72506609848824E-14,
                                                                                            'Wh'        => 2.77778049754611E-11,
                                                                                            'wh'        => 2.77778049754611E-11,
                                                                                            'flb'        => 2.37304336254586E-06,
                                                                                            'BTU'        => 9.47815522922962E-11,
                                                                                            'btu'        => 9.47815522922962E-11
                                                                                        ),
                                                                        'c'        => array(    'J'            => 4.18399101363672E+00,
                                                                                            'e'            => 4.18398900257312E+07,
                                                                                            'c'            => 1.0,
                                                                                            'cal'        => 9.99330315287563E-01,
                                                                                            'eV'        => 2.61142000000000E+19,
                                                                                            'ev'        => 2.61142000000000E+19,
                                                                                            'HPh'        => 1.55856355899327E-06,
                                                                                            'hh'        => 1.55856355899327E-06,
                                                                                            'Wh'        => 1.16222030532950E-03,
                                                                                            'wh'        => 1.16222030532950E-03,
                                                                                            'flb'        => 9.92878733152102E+01,
                                                                                            'BTU'        => 3.96564972437776E-03,
                                                                                            'btu'        => 3.96564972437776E-03
                                                                                        ),
                                                                        'cal'    => array(    'J'            => 4.18679484613929E+00,
                                                                                            'e'            => 4.18679283372801E+07,
                                                                                            'c'            => 1.00067013349059E+00,
                                                                                            'cal'        => 1.0,
                                                                                            'eV'        => 2.61317000000000E+19,
                                                                                            'ev'        => 2.61317000000000E+19,
                                                                                            'HPh'        => 1.55960800463137E-06,
                                                                                            'hh'        => 1.55960800463137E-06,
                                                                                            'Wh'        => 1.16299914807955E-03,
                                                                                            'wh'        => 1.16299914807955E-03,
                                                                                            'flb'        => 9.93544094443283E+01,
                                                                                            'BTU'        => 3.96830723907002E-03,
                                                                                            'btu'        => 3.96830723907002E-03
                                                                                        ),
                                                                        'eV'    => array(    'J'            => 1.60219000146921E-19,
                                                                                            'e'            => 1.60218923136574E-12,
                                                                                            'c'            => 3.82933423195043E-20,
                                                                                            'cal'        => 3.82676978535648E-20,
                                                                                            'eV'        => 1.0,
                                                                                            'ev'        => 1.0,
                                                                                            'HPh'        => 5.96826078912344E-26,
                                                                                            'hh'        => 5.96826078912344E-26,
                                                                                            'Wh'        => 4.45053000026614E-23,
                                                                                            'wh'        => 4.45053000026614E-23,
                                                                                            'flb'        => 3.80206452103492E-18,
                                                                                            'BTU'        => 1.51857982414846E-22,
                                                                                            'btu'        => 1.51857982414846E-22
                                                                                        ),
                                                                        'ev'    => array(    'J'            => 1.60219000146921E-19,
                                                                                            'e'            => 1.60218923136574E-12,
                                                                                            'c'            => 3.82933423195043E-20,
                                                                                            'cal'        => 3.82676978535648E-20,
                                                                                            'eV'        => 1.0,
                                                                                            'ev'        => 1.0,
                                                                                            'HPh'        => 5.96826078912344E-26,
                                                                                            'hh'        => 5.96826078912344E-26,
                                                                                            'Wh'        => 4.45053000026614E-23,
                                                                                            'wh'        => 4.45053000026614E-23,
                                                                                            'flb'        => 3.80206452103492E-18,
                                                                                            'BTU'        => 1.51857982414846E-22,
                                                                                            'btu'        => 1.51857982414846E-22
                                                                                        ),
                                                                        'HPh'    => array(    'J'            => 2.68451741316170E+06,
                                                                                            'e'            => 2.68451612283024E+13,
                                                                                            'c'            => 6.41616438565991E+05,
                                                                                            'cal'        => 6.41186757845835E+05,
                                                                                            'eV'        => 1.67553000000000E+25,
                                                                                            'ev'        => 1.67553000000000E+25,
                                                                                            'HPh'        => 1.0,
                                                                                            'hh'        => 1.0,
                                                                                            'Wh'        => 7.45699653134593E+02,
                                                                                            'wh'        => 7.45699653134593E+02,
                                                                                            'flb'        => 6.37047316692964E+07,
                                                                                            'BTU'        => 2.54442605275546E+03,
                                                                                            'btu'        => 2.54442605275546E+03
                                                                                        ),
                                                                        'hh'    => array(    'J'            => 2.68451741316170E+06,
                                                                                            'e'            => 2.68451612283024E+13,
                                                                                            'c'            => 6.41616438565991E+05,
                                                                                            'cal'        => 6.41186757845835E+05,
                                                                                            'eV'        => 1.67553000000000E+25,
                                                                                            'ev'        => 1.67553000000000E+25,
                                                                                            'HPh'        => 1.0,
                                                                                            'hh'        => 1.0,
                                                                                            'Wh'        => 7.45699653134593E+02,
                                                                                            'wh'        => 7.45699653134593E+02,
                                                                                            'flb'        => 6.37047316692964E+07,
                                                                                            'BTU'        => 2.54442605275546E+03,
                                                                                            'btu'        => 2.54442605275546E+03
                                                                                        ),
                                                                        'Wh'    => array(    'J'            => 3.59999820554720E+03,
                                                                                            'e'            => 3.59999647518369E+10,
                                                                                            'c'            => 8.60422069219046E+02,
                                                                                            'cal'        => 8.59845857713046E+02,
                                                                                            'eV'        => 2.24692340000000E+22,
                                                                                            'ev'        => 2.24692340000000E+22,
                                                                                            'HPh'        => 1.34102248243839E-03,
                                                                                            'hh'        => 1.34102248243839E-03,
                                                                                            'Wh'        => 1.0,
                                                                                            'wh'        => 1.0,
                                                                                            'flb'        => 8.54294774062316E+04,
                                                                                            'BTU'        => 3.41213254164705E+00,
                                                                                            'btu'        => 3.41213254164705E+00
                                                                                        ),
                                                                        'wh'    => array(    'J'            => 3.59999820554720E+03,
                                                                                            'e'            => 3.59999647518369E+10,
                                                                                            'c'            => 8.60422069219046E+02,
                                                                                            'cal'        => 8.59845857713046E+02,
                                                                                            'eV'        => 2.24692340000000E+22,
                                                                                            'ev'        => 2.24692340000000E+22,
                                                                                            'HPh'        => 1.34102248243839E-03,
                                                                                            'hh'        => 1.34102248243839E-03,
                                                                                            'Wh'        => 1.0,
                                                                                            'wh'        => 1.0,
                                                                                            'flb'        => 8.54294774062316E+04,
                                                                                            'BTU'        => 3.41213254164705E+00,
                                                                                            'btu'        => 3.41213254164705E+00
                                                                                        ),
                                                                        'flb'    => array(    'J'            => 4.21400003236424E-02,
                                                                                            'e'            => 4.21399800687660E+05,
                                                                                            'c'            => 1.00717234301644E-02,
                                                                                            'cal'        => 1.00649785509554E-02,
                                                                                            'eV'        => 2.63015000000000E+17,
                                                                                            'ev'        => 2.63015000000000E+17,
                                                                                            'HPh'        => 1.56974211145130E-08,
                                                                                            'hh'        => 1.56974211145130E-08,
                                                                                            'Wh'        => 1.17055614802000E-05,
                                                                                            'wh'        => 1.17055614802000E-05,
                                                                                            'flb'        => 1.0,
                                                                                            'BTU'        => 3.99409272448406E-05,
                                                                                            'btu'        => 3.99409272448406E-05
                                                                                        ),
                                                                        'BTU'    => array(    'J'            => 1.05505813786749E+03,
                                                                                            'e'            => 1.05505763074665E+10,
                                                                                            'c'            => 2.52165488508168E+02,
                                                                                            'cal'        => 2.51996617135510E+02,
                                                                                            'eV'        => 6.58510000000000E+21,
                                                                                            'ev'        => 6.58510000000000E+21,
                                                                                            'HPh'        => 3.93015941224568E-04,
                                                                                            'hh'        => 3.93015941224568E-04,
                                                                                            'Wh'        => 2.93071851047526E-01,
                                                                                            'wh'        => 2.93071851047526E-01,
                                                                                            'flb'        => 2.50369750774671E+04,
                                                                                            'BTU'        => 1.0,
                                                                                            'btu'        => 1.0,
                                                                                        ),
                                                                        'btu'    => array(    'J'            => 1.05505813786749E+03,
                                                                                            'e'            => 1.05505763074665E+10,
                                                                                            'c'            => 2.52165488508168E+02,
                                                                                            'cal'        => 2.51996617135510E+02,
                                                                                            'eV'        => 6.58510000000000E+21,
                                                                                            'ev'        => 6.58510000000000E+21,
                                                                                            'HPh'        => 3.93015941224568E-04,
                                                                                            'hh'        => 3.93015941224568E-04,
                                                                                            'Wh'        => 2.93071851047526E-01,
                                                                                            'wh'        => 2.93071851047526E-01,
                                                                                            'flb'        => 2.50369750774671E+04,
                                                                                            'BTU'        => 1.0,
                                                                                            'btu'        => 1.0,
                                                                                        )
                                                                    ),
                                                'Power'        => array(    'HP'    => array(    'HP'        => 1.0,
                                                                                            'h'            => 1.0,
                                                                                            'W'            => 7.45701000000000E+02,
                                                                                            'w'            => 7.45701000000000E+02
                                                                                        ),
                                                                        'h'        => array(    'HP'        => 1.0,
                                                                                            'h'            => 1.0,
                                                                                            'W'            => 7.45701000000000E+02,
                                                                                            'w'            => 7.45701000000000E+02
                                                                                        ),
                                                                        'W'        => array(    'HP'        => 1.34102006031908E-03,
                                                                                            'h'            => 1.34102006031908E-03,
                                                                                            'W'            => 1.0,
                                                                                            'w'            => 1.0
                                                                                        ),
                                                                        'w'        => array(    'HP'        => 1.34102006031908E-03,
                                                                                            'h'            => 1.34102006031908E-03,
                                                                                            'W'            => 1.0,
                                                                                            'w'            => 1.0
                                                                                        )
                                                                    ),
                                                'Magnetism'    => array(    'T'        => array(    'T'            => 1.0,
                                                                                            'ga'        => 10000.0
                                                                                        ),
                                                                        'ga'    => array(    'T'            => 0.0001,
                                                                                            'ga'        => 1.0
                                                                                        )
                                                                    ),
                                                'Liquid'    => array(    'tsp'    => array(    'tsp'        => 1.0,
                                                                                            'tbs'        => 3.33333333333333E-01,
                                                                                            'oz'        => 1.66666666666667E-01,
                                                                                            'cup'        => 2.08333333333333E-02,
                                                                                            'pt'        => 1.04166666666667E-02,
                                                                                            'us_pt'        => 1.04166666666667E-02,
                                                                                            'uk_pt'        => 8.67558516821960E-03,
                                                                                            'qt'        => 5.20833333333333E-03,
                                                                                            'gal'        => 1.30208333333333E-03,
                                                                                            'l'            => 4.92999408400710E-03,
                                                                                            'lt'        => 4.92999408400710E-03
                                                                                        ),
                                                                        'tbs'    => array(    'tsp'        => 3.00000000000000E+00,
                                                                                            'tbs'        => 1.0,
                                                                                            'oz'        => 5.00000000000000E-01,
                                                                                            'cup'        => 6.25000000000000E-02,
                                                                                            'pt'        => 3.12500000000000E-02,
                                                                                            'us_pt'        => 3.12500000000000E-02,
                                                                                            'uk_pt'        => 2.60267555046588E-02,
                                                                                            'qt'        => 1.56250000000000E-02,
                                                                                            'gal'        => 3.90625000000000E-03,
                                                                                            'l'            => 1.47899822520213E-02,
                                                                                            'lt'        => 1.47899822520213E-02
                                                                                        ),
                                                                        'oz'    => array(    'tsp'        => 6.00000000000000E+00,
                                                                                            'tbs'        => 2.00000000000000E+00,
                                                                                            'oz'        => 1.0,
                                                                                            'cup'        => 1.25000000000000E-01,
                                                                                            'pt'        => 6.25000000000000E-02,
                                                                                            'us_pt'        => 6.25000000000000E-02,
                                                                                            'uk_pt'        => 5.20535110093176E-02,
                                                                                            'qt'        => 3.12500000000000E-02,
                                                                                            'gal'        => 7.81250000000000E-03,
                                                                                            'l'            => 2.95799645040426E-02,
                                                                                            'lt'        => 2.95799645040426E-02
                                                                                        ),
                                                                        'cup'    => array(    'tsp'        => 4.80000000000000E+01,
                                                                                            'tbs'        => 1.60000000000000E+01,
                                                                                            'oz'        => 8.00000000000000E+00,
                                                                                            'cup'        => 1.0,
                                                                                            'pt'        => 5.00000000000000E-01,
                                                                                            'us_pt'        => 5.00000000000000E-01,
                                                                                            'uk_pt'        => 4.16428088074541E-01,
                                                                                            'qt'        => 2.50000000000000E-01,
                                                                                            'gal'        => 6.25000000000000E-02,
                                                                                            'l'            => 2.36639716032341E-01,
                                                                                            'lt'        => 2.36639716032341E-01
                                                                                        ),
                                                                        'pt'    => array(    'tsp'        => 9.60000000000000E+01,
                                                                                            'tbs'        => 3.20000000000000E+01,
                                                                                            'oz'        => 1.60000000000000E+01,
                                                                                            'cup'        => 2.00000000000000E+00,
                                                                                            'pt'        => 1.0,
                                                                                            'us_pt'        => 1.0,
                                                                                            'uk_pt'        => 8.32856176149081E-01,
                                                                                            'qt'        => 5.00000000000000E-01,
                                                                                            'gal'        => 1.25000000000000E-01,
                                                                                            'l'            => 4.73279432064682E-01,
                                                                                            'lt'        => 4.73279432064682E-01
                                                                                        ),
                                                                        'us_pt'    => array(    'tsp'        => 9.60000000000000E+01,
                                                                                            'tbs'        => 3.20000000000000E+01,
                                                                                            'oz'        => 1.60000000000000E+01,
                                                                                            'cup'        => 2.00000000000000E+00,
                                                                                            'pt'        => 1.0,
                                                                                            'us_pt'        => 1.0,
                                                                                            'uk_pt'        => 8.32856176149081E-01,
                                                                                            'qt'        => 5.00000000000000E-01,
                                                                                            'gal'        => 1.25000000000000E-01,
                                                                                            'l'            => 4.73279432064682E-01,
                                                                                            'lt'        => 4.73279432064682E-01
                                                                                        ),
                                                                        'uk_pt'    => array(    'tsp'        => 1.15266000000000E+02,
                                                                                            'tbs'        => 3.84220000000000E+01,
                                                                                            'oz'        => 1.92110000000000E+01,
                                                                                            'cup'        => 2.40137500000000E+00,
                                                                                            'pt'        => 1.20068750000000E+00,
                                                                                            'us_pt'        => 1.20068750000000E+00,
                                                                                            'uk_pt'        => 1.0,
                                                                                            'qt'        => 6.00343750000000E-01,
                                                                                            'gal'        => 1.50085937500000E-01,
                                                                                            'l'            => 5.68260698087162E-01,
                                                                                            'lt'        => 5.68260698087162E-01
                                                                                        ),
                                                                        'qt'    => array(    'tsp'        => 1.92000000000000E+02,
                                                                                            'tbs'        => 6.40000000000000E+01,
                                                                                            'oz'        => 3.20000000000000E+01,
                                                                                            'cup'        => 4.00000000000000E+00,
                                                                                            'pt'        => 2.00000000000000E+00,
                                                                                            'us_pt'        => 2.00000000000000E+00,
                                                                                            'uk_pt'        => 1.66571235229816E+00,
                                                                                            'qt'        => 1.0,
                                                                                            'gal'        => 2.50000000000000E-01,
                                                                                            'l'            => 9.46558864129363E-01,
                                                                                            'lt'        => 9.46558864129363E-01
                                                                                        ),
                                                                        'gal'    => array(    'tsp'        => 7.68000000000000E+02,
                                                                                            'tbs'        => 2.56000000000000E+02,
                                                                                            'oz'        => 1.28000000000000E+02,
                                                                                            'cup'        => 1.60000000000000E+01,
                                                                                            'pt'        => 8.00000000000000E+00,
                                                                                            'us_pt'        => 8.00000000000000E+00,
                                                                                            'uk_pt'        => 6.66284940919265E+00,
                                                                                            'qt'        => 4.00000000000000E+00,
                                                                                            'gal'        => 1.0,
                                                                                            'l'            => 3.78623545651745E+00,
                                                                                            'lt'        => 3.78623545651745E+00
                                                                                        ),
                                                                        'l'        => array(    'tsp'        => 2.02840000000000E+02,
                                                                                            'tbs'        => 6.76133333333333E+01,
                                                                                            'oz'        => 3.38066666666667E+01,
                                                                                            'cup'        => 4.22583333333333E+00,
                                                                                            'pt'        => 2.11291666666667E+00,
                                                                                            'us_pt'        => 2.11291666666667E+00,
                                                                                            'uk_pt'        => 1.75975569552166E+00,
                                                                                            'qt'        => 1.05645833333333E+00,
                                                                                            'gal'        => 2.64114583333333E-01,
                                                                                            'l'            => 1.0,
                                                                                            'lt'        => 1.0
                                                                                        ),
                                                                        'lt'    => array(    'tsp'        => 2.02840000000000E+02,
                                                                                            'tbs'        => 6.76133333333333E+01,
                                                                                            'oz'        => 3.38066666666667E+01,
                                                                                            'cup'        => 4.22583333333333E+00,
                                                                                            'pt'        => 2.11291666666667E+00,
                                                                                            'us_pt'        => 2.11291666666667E+00,
                                                                                            'uk_pt'        => 1.75975569552166E+00,
                                                                                            'qt'        => 1.05645833333333E+00,
                                                                                            'gal'        => 2.64114583333333E-01,
                                                                                            'l'            => 1.0,
                                                                                            'lt'        => 1.0
                                                                                        )
                                                                    )
                                            );


    public static function _parseComplex($complexNumber) {
        $workString = (string) $complexNumber;

        $realNumber = $imaginary = 0;
        //    Extract the suffix, if there is one
        $suffix = substr($workString,-1);
        if (!is_numeric($suffix)) {
            $workString = substr($workString,0,-1);
        } else {
            $suffix = '';
        }

        //    Split the input into its Real and Imaginary components
        $leadingSign = 0;
        if (strlen($workString) > 0) {
            $leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
        }
        $power = '';
        $realNumber = strtok($workString, '+-');
        if (strtoupper(substr($realNumber,-1)) == 'E') {
            $power = strtok('+-');
            ++$leadingSign;
        }

        $realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);

        if ($suffix != '') {
            $imaginary = substr($workString,strlen($realNumber));

            if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
                $imaginary = $realNumber.'1';
                $realNumber = '0';
            } else if ($imaginary == '') {
                $imaginary = $realNumber;
                $realNumber = '0';
            } elseif (($imaginary == '+') || ($imaginary == '-')) {
                $imaginary .= '1';
            }
        }

        return array( 'real'        => $realNumber,
                      'imaginary'    => $imaginary,
                      'suffix'        => $suffix
                    );
    }    //    function _parseComplex()


    private static function _cleanComplex($complexNumber) {
        if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
        if ($complexNumber{0} == '0') $complexNumber = substr($complexNumber,1);
        if ($complexNumber{0} == '.') $complexNumber = '0'.$complexNumber;
        if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
        return $complexNumber;
    }


    private static function _nbrConversionFormat($xVal,$places) {
        if (!is_null($places)) {
            if (strlen($xVal) <= $places) {
                return substr(str_pad($xVal,$places,'0',STR_PAD_LEFT),-10);
            } else {
                return PHPExcel_Calculation_Functions::NaN();
            }
        }

        return substr($xVal,-10);
    }    //    function _nbrConversionFormat()


    /**
     * BESSELI
     *
     * Returns the modified Bessel function, which is equivalent to the Bessel function evaluated for purely imaginary arguments
     *
     * @param    float        $x
     * @param    float        $n
     * @return    int
     */
    public static function BESSELI($x, $n) {
        $x    = (is_null($x))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $n    = (is_null($n))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($n);

        if ((is_numeric($x)) && (is_numeric($n))) {
            $n    = floor($n);
            if ($n < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $f_2_PI = 2 * M_PI;

            if (abs($x) <= 30) {
                $fTerm = pow($x / 2, $n) / PHPExcel_Calculation_MathTrig::FACT($n);
                $nK = 1;
                $fResult = $fTerm;
                $fSqrX = ($x * $x) / 4;
                do {
                    $fTerm *= $fSqrX;
                    $fTerm /= ($nK * ($nK + $n));
                    $fResult += $fTerm;
                } while ((abs($fTerm) > 1e-10) && (++$nK < 100));
            } else {
                $fXAbs = abs($x);
                $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
                if (($n && 1) && ($x < 0)) {
                    $fResult = -$fResult;
                }
            }
            return $fResult;
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function BESSELI()


    /**
     * BESSELJ
     *
     * Returns the Bessel function
     *
     * @param    float        $x
     * @param    float        $n
     * @return    int
     */
    public static function BESSELJ($x, $n) {
        $x    = (is_null($x))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $n    = (is_null($n))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($n);

        if ((is_numeric($x)) && (is_numeric($n))) {
            $n    = floor($n);
            if ($n < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $f_PI_DIV_2 = M_PI / 2;
            $f_PI_DIV_4 = M_PI / 4;

            $fResult = 0;
            if (abs($x) <= 30) {
                $fTerm = pow($x / 2, $n) / PHPExcel_Calculation_MathTrig::FACT($n);
                $nK = 1;
                $fResult = $fTerm;
                $fSqrX = ($x * $x) / -4;
                do {
                    $fTerm *= $fSqrX;
                    $fTerm /= ($nK * ($nK + $n));
                    $fResult += $fTerm;
                } while ((abs($fTerm) > 1e-10) && (++$nK < 100));
            } else {
                $fXAbs = abs($x);
                $fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $n * $f_PI_DIV_2 - $f_PI_DIV_4);
                if (($n && 1) && ($x < 0)) {
                    $fResult = -$fResult;
                }
            }
            return $fResult;
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function BESSELJ()


    private static function _Besselk0($fNum) {
        if ($fNum <= 2) {
            $fNum2 = $fNum * 0.5;
            $y = ($fNum2 * $fNum2);
            $fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
                    (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
                    (0.10750e-3 + $y * 0.74e-5))))));
        } else {
            $y = 2 / $fNum;
            $fRet = exp(-$fNum) / sqrt($fNum) *
                    (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
                    (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
        }
        return $fRet;
    }    //    function _Besselk0()


    private static function _Besselk1($fNum) {
        if ($fNum <= 2) {
            $fNum2 = $fNum * 0.5;
            $y = ($fNum2 * $fNum2);
            $fRet = log($fNum2) * self::BESSELI($fNum, 1) +
                    (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
                    (-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
        } else {
            $y = 2 / $fNum;
            $fRet = exp(-$fNum) / sqrt($fNum) *
                    (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
                    (0.325614e-2 + $y * (-0.68245e-3)))))));
        }
        return $fRet;
    }    //    function _Besselk1()


    /**
     * BESSELK
     *
     * Returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.
     *
     * @param    float        $x
     * @param    float        $ord
     * @return    float
     */
    public static function BESSELK($x, $ord) {
        $x        = (is_null($x))        ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);

        if ((is_numeric($x)) && (is_numeric($ord))) {
            if (($ord < 0) || ($x == 0.0)) {
                return PHPExcel_Calculation_Functions::NaN();
            }

            switch(floor($ord)) {
                case 0 :    return self::_Besselk0($x);
                            break;
                case 1 :    return self::_Besselk1($x);
                            break;
                default :    $fTox    = 2 / $x;
                            $fBkm    = self::_Besselk0($x);
                            $fBk    = self::_Besselk1($x);
                            for ($n = 1; $n < $ord; ++$n) {
                                $fBkp    = $fBkm + $n * $fTox * $fBk;
                                $fBkm    = $fBk;
                                $fBk    = $fBkp;
                            }
            }
            return $fBk;
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function BESSELK()


    private static function _Bessely0($fNum) {
        if ($fNum < 8.0) {
            $y = ($fNum * $fNum);
            $f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
            $f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
            $fRet = $f1 / $f2 + M_2DIVPI * self::BESSELJ($fNum, 0) * log($fNum);
        } else {
            $z = 8.0 / $fNum;
            $y = ($z * $z);
            $xx = $fNum - 0.785398164;
            $f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
            $f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
            $fRet = sqrt(M_2DIVPI / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
        }
        return $fRet;
    }    //    function _Bessely0()


    private static function _Bessely1($fNum) {
        if ($fNum < 8.0) {
            $y = ($fNum * $fNum);
            $f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
                (-0.4237922726e7 + $y * 0.8511937935e4)))));
            $f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
                (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
            $fRet = $f1 / $f2 + M_2DIVPI * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
        } else {
            $z = 8.0 / $fNum;
            $y = ($z * $z);
            $xx = $fNum - 2.356194491;
            $f1 = 1 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e6))));
            $f2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y * (-0.88228987e-6 + $y * 0.105787412e-6)));
            $fRet = sqrt(M_2DIVPI / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
            #i12430# ...but this seems to work much better.
//            $fRet = sqrt(M_2DIVPI / $fNum) * sin($fNum - 2.356194491);
        }
        return $fRet;
    }    //    function _Bessely1()


    /**
     * BESSELY
     *
     * Returns the Bessel function, which is also called the Weber function or the Neumann function.
     *
     * @param    float        $x
     * @param    float        $n
     * @return    int
     */
    public static function BESSELY($x, $ord) {
        $x        = (is_null($x))        ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);

        if ((is_numeric($x)) && (is_numeric($ord))) {
            if (($ord < 0) || ($x == 0.0)) {
                return PHPExcel_Calculation_Functions::NaN();
            }

            switch(floor($ord)) {
                case 0 :    return self::_Bessely0($x);
                            break;
                case 1 :    return self::_Bessely1($x);
                            break;
                default:    $fTox    = 2 / $x;
                            $fBym    = self::_Bessely0($x);
                            $fBy    = self::_Bessely1($x);
                            for ($n = 1; $n < $ord; ++$n) {
                                $fByp    = $n * $fTox * $fBy - $fBym;
                                $fBym    = $fBy;
                                $fBy    = $fByp;
                            }
            }
            return $fBy;
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function BESSELY()


    /**
     * BINTODEC
     *
     * Return a binary value as Decimal.
     *
     * @param    string        $x
     * @return    string
     */
    public static function BINTODEC($x) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
            $x = floor($x);
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        if (strlen($x) > 10) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (strlen($x) == 10) {
            //    Two's Complement
            $x = substr($x,-9);
            return '-'.(512-bindec($x));
        }
        return bindec($x);
    }    //    function BINTODEC()


    /**
     * BINTOHEX
     *
     * Return a binary value as Hex.
     *
     * @param    string        $x
     * @return    string
     */
    public static function BINTOHEX($x, $places=null) {
        $x    = floor(PHPExcel_Calculation_Functions::flattenSingleValue($x));
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
            $x = floor($x);
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        if (strlen($x) > 10) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (strlen($x) == 10) {
            //    Two's Complement
            return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
        }
        $hexVal = (string) strtoupper(dechex(bindec($x)));

        return self::_nbrConversionFormat($hexVal,$places);
    }    //    function BINTOHEX()


    /**
     * BINTOOCT
     *
     * Return a binary value as Octal.
     *
     * @param    string        $x
     * @return    string
     */
    public static function BINTOOCT($x, $places=null) {
        $x    = floor(PHPExcel_Calculation_Functions::flattenSingleValue($x));
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
            $x = floor($x);
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        if (strlen($x) > 10) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (strlen($x) == 10) {
            //    Two's Complement
            return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
        }
        $octVal = (string) decoct(bindec($x));

        return self::_nbrConversionFormat($octVal,$places);
    }    //    function BINTOOCT()


    /**
     * DECTOBIN
     *
     * Return an octal value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function DECTOBIN($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) floor($x);
        $r = decbin($x);
        if (strlen($r) == 32) {
            //    Two's Complement
            $r = substr($r,-10);
        } elseif (strlen($r) > 11) {
            return PHPExcel_Calculation_Functions::NaN();
        }

        return self::_nbrConversionFormat($r,$places);
    }    //    function DECTOBIN()


    /**
     * DECTOHEX
     *
     * Return an octal value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function DECTOHEX($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) floor($x);
        $r = strtoupper(dechex($x));
        if (strlen($r) == 8) {
            //    Two's Complement
            $r = 'FF'.$r;
        }

        return self::_nbrConversionFormat($r,$places);
    }    //    function DECTOHEX()


    /**
     * DECTOOCT
     *
     * Return an octal value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function DECTOOCT($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                $x = (int) $x;
            } else {
                return PHPExcel_Calculation_Functions::VALUE();
            }
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) floor($x);
        $r = decoct($x);
        if (strlen($r) == 11) {
            //    Two's Complement
            $r = substr($r,-10);
        }

        return self::_nbrConversionFormat($r,$places);
    }    //    function DECTOOCT()


    /**
     * HEXTOBIN
     *
     * Return a hex value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function HEXTOBIN($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        $binVal = decbin(hexdec($x));

        return substr(self::_nbrConversionFormat($binVal,$places),-10);
    }    //    function HEXTOBIN()


    /**
     * HEXTODEC
     *
     * Return a hex value as octal.
     *
     * @param    string        $x
     * @return    string
     */
    public static function HEXTODEC($x) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        return hexdec($x);
    }    //    function HEXTODEC()


    /**
     * HEXTOOCT
     *
     * Return a hex value as octal.
     *
     * @param    string        $x
     * @return    string
     */
    public static function HEXTOOCT($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        $octVal = decoct(hexdec($x));

        return self::_nbrConversionFormat($octVal,$places);
    }    //    function HEXTOOCT()


    /**
     * OCTTOBIN
     *
     * Return an octal value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function OCTTOBIN($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        $r = decbin(octdec($x));

        return self::_nbrConversionFormat($r,$places);
    }    //    function OCTTOBIN()


    /**
     * OCTTODEC
     *
     * Return an octal value as binary.
     *
     * @param    string        $x
     * @return    string
     */
    public static function OCTTODEC($x) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        return octdec($x);
    }    //    function OCTTODEC()


    /**
     * OCTTOHEX
     *
     * Return an octal value as hex.
     *
     * @param    string        $x
     * @return    string
     */
    public static function OCTTOHEX($x, $places=null) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
        $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);

        if (is_bool($x)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $x = (string) $x;
        if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        $hexVal = strtoupper(dechex(octdec($x)));

        return self::_nbrConversionFormat($hexVal,$places);
    }    //    function OCTTOHEX()


    /**
     * COMPLEX
     *
     * returns a complex number of the form x + yi or x + yj.
     *
     * @param    float        $realNumber
     * @param    float        $imaginary
     * @param    string        $suffix
     * @return    string
     */
    public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
        $realNumber    = (is_null($realNumber))    ? 0.0 :    (float) PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
        $imaginary    = (is_null($imaginary))        ? 0.0 :    (float) PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
        $suffix        = (is_null($suffix))        ? 'i' :    PHPExcel_Calculation_Functions::flattenSingleValue($suffix);

        if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
            (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
            if ($suffix == '') $suffix = 'i';
            if ($realNumber == 0.0) {
                if ($imaginary == 0.0) {
                    return (string) '0';
                } elseif ($imaginary == 1.0) {
                    return (string) $suffix;
                } elseif ($imaginary == -1.0) {
                    return (string) '-'.$suffix;
                }
                return (string) $imaginary.$suffix;
            } elseif ($imaginary == 0.0) {
                return (string) $realNumber;
            } elseif ($imaginary == 1.0) {
                return (string) $realNumber.'+'.$suffix;
            } elseif ($imaginary == -1.0) {
                return (string) $realNumber.'-'.$suffix;
            }
            if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
            return (string) $realNumber.$imaginary.$suffix;
        }

        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function COMPLEX()


    /**
     * IMAGINARY
     *
     * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    real
     */
    public static function IMAGINARY($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }
        return $parsedComplex['imaginary'];
    }    //    function IMAGINARY()


    /**
     * IMREAL
     *
     * Returns the real coefficient of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    real
     */
    public static function IMREAL($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }
        return $parsedComplex['real'];
    }    //    function IMREAL()


    /**
     * IMABS
     *
     * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    real
     */
    public static function IMABS($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }
        return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
    }    //    function IMABS()


    /**
     * IMARGUMENT
     *
     * Returns the argument theta of a complex number, i.e. the angle in radians from the real axis to the representation of the number in polar coordinates.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMARGUMENT($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if ($parsedComplex['real'] == 0.0) {
            if ($parsedComplex['imaginary'] == 0.0) {
                return 0.0;
            } elseif($parsedComplex['imaginary'] < 0.0) {
                return M_PI / -2;
            } else {
                return M_PI / 2;
            }
        } elseif ($parsedComplex['real'] > 0.0) {
            return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
        } elseif ($parsedComplex['imaginary'] < 0.0) {
            return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
        } else {
            return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
        }
    }    //    function IMARGUMENT()


    /**
     * IMCONJUGATE
     *
     * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMCONJUGATE($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);

        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if ($parsedComplex['imaginary'] == 0.0) {
            return $parsedComplex['real'];
        } else {
            return self::_cleanComplex(self::COMPLEX($parsedComplex['real'], 0 - $parsedComplex['imaginary'], $parsedComplex['suffix']));
        }
    }    //    function IMCONJUGATE()


    /**
     * IMCOS
     *
     * Returns the cosine of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMCOS($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if ($parsedComplex['imaginary'] == 0.0) {
            return cos($parsedComplex['real']);
        } else {
            return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
        }
    }    //    function IMCOS()


    /**
     * IMSIN
     *
     * Returns the sine of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMSIN($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if ($parsedComplex['imaginary'] == 0.0) {
            return sin($parsedComplex['real']);
        } else {
            return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
        }
    }    //    function IMSIN()


    /**
     * IMSQRT
     *
     * Returns the square root of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMSQRT($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        $theta = self::IMARGUMENT($complexNumber);
        $d1 = cos($theta / 2);
        $d2 = sin($theta / 2);
        $r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));

        if ($parsedComplex['suffix'] == '') {
            return self::COMPLEX($d1 * $r,$d2 * $r);
        } else {
            return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
        }
    }    //    function IMSQRT()


    /**
     * IMLN
     *
     * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMLN($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return PHPExcel_Calculation_Functions::NaN();
        }

        $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
        $t = self::IMARGUMENT($complexNumber);

        if ($parsedComplex['suffix'] == '') {
            return self::COMPLEX($logR,$t);
        } else {
            return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
        }
    }    //    function IMLN()


    /**
     * IMLOG10
     *
     * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMLOG10($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return log10($parsedComplex['real']);
        }

        return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
    }    //    function IMLOG10()


    /**
     * IMLOG2
     *
     * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMLOG2($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return log($parsedComplex['real'],2);
        }

        return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
    }    //    function IMLOG2()


    /**
     * IMEXP
     *
     * Returns the exponential of a complex number in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMEXP($complexNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
            return '1';
        }

        $e = exp($parsedComplex['real']);
        $eX = $e * cos($parsedComplex['imaginary']);
        $eY = $e * sin($parsedComplex['imaginary']);

        if ($parsedComplex['suffix'] == '') {
            return self::COMPLEX($eX,$eY);
        } else {
            return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
        }
    }    //    function IMEXP()


    /**
     * IMPOWER
     *
     * Returns a complex number in x + yi or x + yj text format raised to a power.
     *
     * @param    string        $complexNumber
     * @return    string
     */
    public static function IMPOWER($complexNumber,$realNumber) {
        $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
        $realNumber        = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);

        if (!is_numeric($realNumber)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }

        $parsedComplex = self::_parseComplex($complexNumber);
        if (!is_array($parsedComplex)) {
            return $parsedComplex;
        }

        $r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
        $rPower = pow($r,$realNumber);
        $theta = self::IMARGUMENT($complexNumber) * $realNumber;
        if ($theta == 0) {
            return 1;
        } elseif ($parsedComplex['imaginary'] == 0.0) {
            return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
        } else {
            return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
        }
    }    //    function IMPOWER()


    /**
     * IMDIV
     *
     * Returns the quotient of two complex numbers in x + yi or x + yj text format.
     *
     * @param    string        $complexDividend
     * @param    string        $complexDivisor
     * @return    real
     */
    public static function IMDIV($complexDividend,$complexDivisor) {
        $complexDividend    = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
        $complexDivisor    = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);

        $parsedComplexDividend = self::_parseComplex($complexDividend);
        if (!is_array($parsedComplexDividend)) {
            return $parsedComplexDividend;
        }

        $parsedComplexDivisor = self::_parseComplex($complexDivisor);
        if (!is_array($parsedComplexDivisor)) {
            return $parsedComplexDividend;
        }

        if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
            ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
            return PHPExcel_Calculation_Functions::NaN();
        }
        if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
            $parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
        }

        $d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
        $d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
        $d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);

        $r = $d1/$d3;
        $i = $d2/$d3;

        if ($i > 0.0) {
            return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
        } elseif ($i < 0.0) {
            return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
        } else {
            return $r;
        }
    }    //    function IMDIV()


    /**
     * IMSUB
     *
     * Returns the difference of two complex numbers in x + yi or x + yj text format.
     *
     * @param    string        $complexNumber1
     * @param    string        $complexNumber2
     * @return    real
     */
    public static function IMSUB($complexNumber1,$complexNumber2) {
        $complexNumber1    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
        $complexNumber2    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);

        $parsedComplex1 = self::_parseComplex($complexNumber1);
        if (!is_array($parsedComplex1)) {
            return $parsedComplex1;
        }

        $parsedComplex2 = self::_parseComplex($complexNumber2);
        if (!is_array($parsedComplex2)) {
            return $parsedComplex2;
        }

        if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
            ($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
            return PHPExcel_Calculation_Functions::NaN();
        } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
            $parsedComplex1['suffix'] = $parsedComplex2['suffix'];
        }

        $d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
        $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];

        return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
    }    //    function IMSUB()


    /**
     * IMSUM
     *
     * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
     *
     * @param    array of mixed        Data Series
     * @return    real
     */
    public static function IMSUM() {
        // Return value
        $returnValue = self::_parseComplex('0');
        $activeSuffix = '';

        // Loop through the arguments
        $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
        foreach ($aArgs as $arg) {
            $parsedComplex = self::_parseComplex($arg);
            if (!is_array($parsedComplex)) {
                return $parsedComplex;
            }

            if ($activeSuffix == '') {
                $activeSuffix = $parsedComplex['suffix'];
            } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                return PHPExcel_Calculation_Functions::VALUE();
            }

            $returnValue['real'] += $parsedComplex['real'];
            $returnValue['imaginary'] += $parsedComplex['imaginary'];
        }

        if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
        return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
    }    //    function IMSUM()


    /**
     * IMPRODUCT
     *
     * Returns the product of two or more complex numbers in x + yi or x + yj text format.
     *
     * @param    array of mixed        Data Series
     * @return    real
     */
    public static function IMPRODUCT() {
        // Return value
        $returnValue = self::_parseComplex('1');
        $activeSuffix = '';

        // Loop through the arguments
        $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
        foreach ($aArgs as $arg) {
            $parsedComplex = self::_parseComplex($arg);
            if (!is_array($parsedComplex)) {
                return $parsedComplex;
            }
            $workValue = $returnValue;
            if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
                $activeSuffix = $parsedComplex['suffix'];
            } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
            $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
        }

        if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
        return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
    }    //    function IMPRODUCT()


    /**
     * DELTA
     *
     * Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
     *
     * @param    float        $a
     * @param    float        $b
     * @return    int
     */
    public static function DELTA($a, $b=0) {
        $a    = PHPExcel_Calculation_Functions::flattenSingleValue($a);
        $b    = PHPExcel_Calculation_Functions::flattenSingleValue($b);

        return (int) ($a == $b);
    }    //    function DELTA()


    /**
     * GESTEP
     *
     * Returns 1 if number = step; returns 0 (zero) otherwise
     *
     * @param    float        $number
     * @param    float        $step
     * @return    int
     */
    public static function GESTEP($number, $step=0) {
        $number    = PHPExcel_Calculation_Functions::flattenSingleValue($number);
        $step    = PHPExcel_Calculation_Functions::flattenSingleValue($step);

        return (int) ($number >= $step);
    }    //    function GESTEP()


    //
    //    Private method to calculate the erf value
    //
    private static $_two_sqrtpi = 1.128379167095512574;

    public static function _erfVal($x) {
        if (abs($x) > 2.2) {
            return 1 - self::_erfcVal($x);
        }
        $sum = $term = $x;
        $xsqr = ($x * $x);
        $j = 1;
        do {
            $term *= $xsqr / $j;
            $sum -= $term / (2 * $j + 1);
            ++$j;
            $term *= $xsqr / $j;
            $sum += $term / (2 * $j + 1);
            ++$j;
            if ($sum == 0.0) {
                break;
            }
        } while (abs($term / $sum) > PRECISION);
        return self::$_two_sqrtpi * $sum;
    }    //    function _erfVal()


    /**
     * ERF
     *
     * Returns the error function integrated between lower_limit and upper_limit
     *
     * @param    float        $lower    lower bound for integrating ERF
     * @param    float        $upper    upper bound for integrating ERF.
     *                                If omitted, ERF integrates between zero and lower_limit
     * @return    int
     */
    public static function ERF($lower, $upper = null) {
        $lower    = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
        $upper    = PHPExcel_Calculation_Functions::flattenSingleValue($upper);

        if (is_numeric($lower)) {
            if ($lower < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if (is_null($upper)) {
                return self::_erfVal($lower);
            }
            if (is_numeric($upper)) {
                if ($upper < 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                return self::_erfVal($upper) - self::_erfVal($lower);
            }
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function ERF()


    //
    //    Private method to calculate the erfc value
    //
    private static $_one_sqrtpi = 0.564189583547756287;

    private static function _erfcVal($x) {
        if (abs($x) < 2.2) {
            return 1 - self::_erfVal($x);
        }
        if ($x < 0) {
            return 2 - self::ERFC(-$x);
        }
        $a = $n = 1;
        $b = $c = $x;
        $d = ($x * $x) + 0.5;
        $q1 = $q2 = $b / $d;
        $t = 0;
        do {
            $t = $a * $n + $b * $x;
            $a = $b;
            $b = $t;
            $t = $c * $n + $d * $x;
            $c = $d;
            $d = $t;
            $n += 0.5;
            $q1 = $q2;
            $q2 = $b / $d;
        } while ((abs($q1 - $q2) / $q2) > PRECISION);
        return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
    }    //    function _erfcVal()


    /**
     * ERFC
     *
     * Returns the complementary ERF function integrated between x and infinity
     *
     * @param    float        $x        The lower bound for integrating ERF
     * @return    int
     */
    public static function ERFC($x) {
        $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);

        if (is_numeric($x)) {
            if ($x < 0) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return self::_erfcVal($x);
        }
        return PHPExcel_Calculation_Functions::VALUE();
    }    //    function ERFC()


    /**
     * getConversionGroups
     *
     * @return    array
     */
    public static function getConversionGroups() {
        $conversionGroups = array();
        foreach(self::$_conversionUnits as $conversionUnit) {
            $conversionGroups[] = $conversionUnit['Group'];
        }
        return array_merge(array_unique($conversionGroups));
    }    //    function getConversionGroups()


    /**
     * getConversionGroupUnits
     *
     * @return    array
     */
    public static function getConversionGroupUnits($group = NULL) {
        $conversionGroups = array();
        foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
            if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
            }
        }
        return $conversionGroups;
    }    //    function getConversionGroupUnits()


    /**
     * getConversionGroupUnitDetails
     *
     * @return    array
     */
    public static function getConversionGroupUnitDetails($group = NULL) {
        $conversionGroups = array();
        foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
            if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                $conversionGroups[$conversionGroup['Group']][] = array(    'unit'            => $conversionUnit,
                                                                        'description'    => $conversionGroup['Unit Name']
                                                                      );
            }
        }
        return $conversionGroups;
    }    //    function getConversionGroupUnitDetails()


    /**
     * getConversionGroups
     *
     * @return    array
     */
    public static function getConversionMultipliers() {
        return self::$_conversionMultipliers;
    }    //    function getConversionGroups()


    /**
     * CONVERTUOM
     *
     * @param    float        $value
     * @param    string        $fromUOM
     * @param    string        $toUOM
     * @return    float
     */
    public static function CONVERTUOM($value, $fromUOM, $toUOM) {
        $value        = PHPExcel_Calculation_Functions::flattenSingleValue($value);
        $fromUOM    = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
        $toUOM        = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);

        if (!is_numeric($value)) {
            return PHPExcel_Calculation_Functions::VALUE();
        }
        $fromMultiplier = 1;
        if (isset(self::$_conversionUnits[$fromUOM])) {
            $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
        } else {
            $fromMultiplier = substr($fromUOM,0,1);
            $fromUOM = substr($fromUOM,1);
            if (isset(self::$_conversionMultipliers[$fromMultiplier])) {
                $fromMultiplier = self::$_conversionMultipliers[$fromMultiplier]['multiplier'];
            } else {
                return PHPExcel_Calculation_Functions::NA();
            }
            if ((isset(self::$_conversionUnits[$fromUOM])) && (self::$_conversionUnits[$fromUOM]['AllowPrefix'])) {
                $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
            } else {
                return PHPExcel_Calculation_Functions::NA();
            }
        }
        $value *= $fromMultiplier;

        $toMultiplier = 1;
        if (isset(self::$_conversionUnits[$toUOM])) {
            $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
        } else {
            $toMultiplier = substr($toUOM,0,1);
            $toUOM = substr($toUOM,1);
            if (isset(self::$_conversionMultipliers[$toMultiplier])) {
                $toMultiplier = self::$_conversionMultipliers[$toMultiplier]['multiplier'];
            } else {
                return PHPExcel_Calculation_Functions::NA();
            }
            if ((isset(self::$_conversionUnits[$toUOM])) && (self::$_conversionUnits[$toUOM]['AllowPrefix'])) {
                $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
            } else {
                return PHPExcel_Calculation_Functions::NA();
            }
        }
        if ($unitGroup1 != $unitGroup2) {
            return PHPExcel_Calculation_Functions::NA();
        }

        if ($fromUOM == $toUOM) {
            return 1.0;
        } elseif ($unitGroup1 == 'Temperature') {
            if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
                if (($toUOM == 'F') || ($toUOM == 'fah')) {
                    return 1.0;
                } else {
                    $value = (($value - 32) / 1.8);
                    if (($toUOM == 'K') || ($toUOM == 'kel')) {
                        $value += 273.15;
                    }
                    return $value;
                }
            } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
                      (($toUOM == 'K') || ($toUOM == 'kel'))) {
                        return 1.0;
            } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
                      (($toUOM == 'C') || ($toUOM == 'cel'))) {
                    return 1.0;
            }
            if (($toUOM == 'F') || ($toUOM == 'fah')) {
                if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
                    $value -= 273.15;
                }
                return ($value * 1.8) + 32;
            }
            if (($toUOM == 'C') || ($toUOM == 'cel')) {
                return $value - 273.15;
            }
            return $value + 273.15;
        }
        return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
    }    //    function CONVERTUOM()

}    //    class PHPExcel_Calculation_Engineering
